45423_C000.fm Page i Monday, August 27, 2007 11:16 AM Half title page PROCESS ENGINEERING and DESIGN USING VISUAL BASIC® 45423_C000.fm Page ii Monday, August 27, 2007 11:16 AM 45423_C000.fm Page iii Monday, August 27, 2007 11:16 AM Title Page PROCESS ENGINEERING and DESIGN USING VISUAL BASIC® ARUN DATTA Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business 45423_C000.fm Page iv Monday, August 27, 2007 11:16 AM Visual Basic and Excel are registered trademarks of Microsoft. CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2008 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed in the United States of America on acid-free paper 10 9 8 7 6 5 4 3 2 1 International Standard Book Number-13: 978-1-4200-4542-0 (Hardcover) This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the conse- quences of their use. 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Library of Congress Cataloging-in-Publication Data Datta, Arun. Process engineering and design using Visual BASIC / Arun Datta. p. cm. Includes bibliographical references and index. ISBN-13: 978-1-4200-4542-0 (alk. paper) ISBN-10: 1-4200-4542-3 (alk. paper) 1. Chemical processes--Mathematical models. 2. Chemical processes--Computer simulation. 3. Microsoft Visual BASIC. I. Title. TP155.7.D36 2006 660’.28--dc22 2006103307 Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com 45423_C000.fm Page v Monday, August 27, 2007 11:16 AM Dedication To my mother Smt. Narayani Datta 45423_C000.fm Page vi Monday, August 27, 2007 11:16 AM 45423_C000.fm Page vii Monday, August 27, 2007 11:16 AM Contents Chapter one Basic mathematics.......................................................................1 Introduction.............................................................................................................1 Physical constants...................................................................................................1 SI prefixes.......................................................................................................1 Mensuration.............................................................................................................2 Triangles..........................................................................................................2 Rectangles.......................................................................................................2 Parallelogram (opposite sides parallel).....................................................3 Rhombus (equilateral parallelogram)........................................................3 Trapezoid (four sides, two parallel)...........................................................3 Quadrilateral (four sided)............................................................................4 Regular polygon of n sides..........................................................................4 Circle................................................................................................................4 Ellipse..............................................................................................................6 Parabola..........................................................................................................6 Prism................................................................................................................6 Pyramid...........................................................................................................7 Right circular cylinder..................................................................................7 Sphere..............................................................................................................7 Right circular cone........................................................................................8 Dished end.....................................................................................................8 Irregular shape...............................................................................................8 Trapezoidal rule.............................................................................................8 Simpson’s rule...............................................................................................8 Irregular volume...........................................................................................9 Algebra.....................................................................................................................9 Factoring.........................................................................................................9 Arithmetic progression.................................................................................9 Geometric progression...............................................................................10 Infinite series (in GP)..................................................................................10 Best fit straight line (least squares method)...........................................10 Binomial equation.......................................................................................11 Polynomial equation...................................................................................11 vii 45423_C000.fm Page viii Monday, August 27, 2007 11:16 AM viii Process engineering and design using Visual Basic Maxima/minima.........................................................................................12 Matrix............................................................................................................13 Addition and multiplication of matrices............................................13 Addition of matrices..............................................................................14 Multiplication of matrices.....................................................................14 Matrix properties involving addition.................................................14 Matrix properties involving multiplication.......................................15 Matrix properties involving addition and multiplication...............15 Transpose.................................................................................................15 Symmetric matrix...................................................................................16 Diagonal matrix......................................................................................16 Determinants................................................................................................16 Properties of determinants....................................................................17 Cofactor....................................................................................................18 Determinant and inverses.....................................................................19 Adjoint......................................................................................................19 Cramer’s rule...............................................................................................20 Trigonometry.........................................................................................................21 Functions of circular trigonometry..........................................................21 Periodic functions.......................................................................................22 The magic identity......................................................................................22 The addition formulas................................................................................23 Double angle and half angle.....................................................................23 Product and sum formulas........................................................................24 Relations between angles and sides of triangles...................................25 Law of sines.................................................................................................26 Law of tangents...........................................................................................26 Law of cosines.............................................................................................26 Other relations.............................................................................................26 Inverse trigonometric functions................................................................27 Hyperbolic functions..................................................................................28 Other hyperbolic functions........................................................................29 Inverse hyperbolic functions.....................................................................29 Analytical geometry.............................................................................................30 Straight line..................................................................................................30 Straight line through two points.........................................................30 Three points on one line.......................................................................31 The circle.......................................................................................................31 Tangent.....................................................................................................31 Normal.....................................................................................................32 Four points on a circle...........................................................................32 Circle through three points...................................................................33 Conic section................................................................................................33 Focus.........................................................................................................33 Eccentricity..............................................................................................33 Directrix....................................................................................................33 45423_C000.fm Page ix Monday, August 27, 2007 11:16 AM Contents ix Partial derivatives...................................................................................33 Parabola....................................................................................................34 Tangent line with a given slope, m.....................................................36 Ellipse.......................................................................................................36 Hyperbola................................................................................................38 Calculus..................................................................................................................40 Differential calculus....................................................................................40 Understanding the derivatives.................................................................41 Standard derivatives...................................................................................42 Integral calculus..........................................................................................44 Volume of horizontal dished end........................................................44 Volume of vertical dished end.............................................................46 Standard integrals.......................................................................................47 Differential equations...........................................................................................48 First-order differential equations..............................................................48 Separation of variables..........................................................................49 Second-order differential equations.........................................................50 Bessel function........................................................................................51 Partial differential equations...............................................................................52 Laplace transform.......................................................................................60 Standard Laplace transforms....................................................................61 Fourier half-range expansions..................................................................62 Fourier half-range cosine series................................................................63 Fourier half-range sine series....................................................................63 Numerical analysis...............................................................................................65 Solving linear equations (Newton’s method).........................................65 Newton’s method in two variables..........................................................66 Numerical methods in linear algebra......................................................68 Gauss elimination...................................................................................68 Cholesky method....................................................................................70 Numerical integration................................................................................72 Trapezoidal rule......................................................................................72 Simpson’s rule.........................................................................................72 Double integration using Simpson’s rule...............................................75 Numerical solution of first-order differential equations......................76 Euler’s method........................................................................................76 Improved Euler’s method.....................................................................76 Runge–Kutta method.............................................................................77 Second-order differential equations.........................................................79 Runge–Kutta–Nystrom method...........................................................79 Partial differential equations.....................................................................81 Heat conduction problem.....................................................................81 Numerical solution.....................................................................................83 Alternating direction implicit (ADI) method....................................85 Equation of state...................................................................................................90 Boyle’s law and Charles’ law....................................................................90